DNS of Turbulent Flows in Ducts with Complex Shape

We carry out Direct Numerical Simulation (DNS) of flows in closed straight ducts with complex peripheral shape. To perform the simulations the Navier-Stokes equations in cylindrical coordinates are discretized by a second-order finite difference scheme, and the immersed-boundary technique is used to resolve the flow close to walls of complex shape. The basic geometry is a circular pipe of radius R, with imposed sinusoidal perturbations of the type ηRsin(Nw𝜃)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\eta R \sin (N_{w}\theta )$\end{document}. Simulations by varying Nw at fixed η were performed to investigate the effect of the perturbation wavenumber. Additional simulations by fixing Nw and varying η also allow to investigate the influence of the amplitude of the wall corrugations. The modifications of the near-wall structures due to change in the shape of the walls are well depicted through contour plots of the radial component of the vorticity. The presence of geometrical disturbances anchors the structures at the locations where curvature changes, and the shape of the structures is strongly linked to the amplitude of the wall corrugation. Our interest is also in understanding the influence of the shape of the surface on wall friction. We were expecting some changes in the profile of the total stress with respect to that of the circular pipe, which instead were not found. This is a first indication that changes in the near-wall region do not affect the outer region, and that Townsend’s similarity hypothesis holds.